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Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that themartingale selection problem is solvable if there exists an adapted sequence ofselectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aimof this note is to underline the connection between this problem and theproblems of asset pricing in general discrete-time market models with portfolioconstraints and transaction costs. For the case of relatively open convex sets$V_t(\omega)$ we present effective necessary and sufficient conditions for thesolvability of a suitably generalized martingale selection problem. We showthat this result allows to obtain computationally feasible formulas for theprice bounds of contingent claims. For the case of currency markets we alsogive a comment on the first fundamental theorem of asset pricing.

Martingale selection problem and asset pricing in finite discrete time